This invention relates to a mode trap to trap and absorb transverse modes in linear accelerators, and more particularly, in wake field accelerators.
A beam in a linear accelerator forms a deflection mode, or transverse field mode, in addition to an accelerator mode. Deflection modes in linear accelerators are generated by deviations of the beam from the geometrical axis.
They are the non-axisymmetric wake fields generated in accelerating cavities via beam misalignment with the cavity axis. Deflection modes result in the phenomena known as beam breakup (BBU) and the head-tail instability, both of which refer to uncontrolled transverse wandering and subsequent loss of the beam, or less severely, emittance degradation. Beam breakup is defined as a cumulative bunch-to-bunch effect, and head-tail is defined as an intra-bunch effect. The spawning of such modes in high-gradient structures will be inevitable given the requisite small-diameter cavity apertures and feasible beam alignment tolerances. Their amplitudes will also be large due to the high luminosities required for physics studies in a TeV electron linear collider.
The build-up of deflection modes in accelerating cavities is a problem in present accelerators and will be a major problem in any future high-gradient linear collider. The deflection mode will create forces on a trailing portion of the beam and subsequent bunches with adverse results.
The approach to the problem of deflection-mode dampening is that of considering eligible modes in slow-wave structures. Accelerating modes are axisymmetric TM.sub.01 in nature, consisting of many axial harmonics in an iris-loaded waveguide, or consisting of one pure mode in a dielectric-lined waveguide. Deflection modes, however, are nonaxisymmetric hybrids containing both axial electric and magnetic fields. These hybrid modes are labeled HEM.sub.mn where m refers to the azimuthal harmonic and n is an ordering index not necessarily referring to radial harmonics. At cutoff, the dispersion relation for these hybrids degenerates to the conventional TM.sub.mn and TE.sub.mn waveguide modes, although the field amplitudes for TE modes are identically zero at cutoff. Of interest here, for dielectric-lined waveguide, are the HEM.sub.11, HEM.sub.21, and HEM.sub.12 modes which correspond to the TE.sub.11, TE.sub.21, and TM.sub.11 modes at cutoff, respectively. Among the physical features that differentiate the hybrid modes from the accelerating modes are obviously the composite electric and magnetic field components. The accelerating modes (TM.sub.01) contain only the E.sub.r, B.sub..theta., and E.sub.Z field components and one of the boundary conditions in dielectric-lined waveguide is Ez=0 at the conducting wall. The subscripts r, .theta., and z, used herein refer to the radial, r, transverse, .theta., and axial z components in a cylindrical coordinate system where E refers to the Electric field components and B refers to the magnetic field components. This is equivalent to B.sub..theta. requiring a surface current K.sub.z on the conducting wall. The hybrid modes, on the other hand, tend to contain all three electric and magnetic field components (E.sub.r, E.sub..theta., E.sub.z, B.sub.r, B.sub..theta., and B.sub.z) and have the additional boundary condition E.sub..theta. =O at the conducting wall which is equivalent to B.sub.z requiring a surface current K.sub..theta. there. This boundary condition can then be exploited to dampen the beam-deflecting hybrid modes by comprising the conducting wall of axial, closely spaced, insulated wires as shown in FIG. 1. The variables a and b indicate regions in the waveguide, relative to the radius r of the cross section of the waveguide of FIG. 1, in which the accelerating modes and hybrid modes may be confined. With such a segmented conductor the accelerating mode (TM.sub.01) will be confined to the regions r&lt;b just as though the wall were a uniform conductor, but the hybrid modes will radiate to the region r&gt;b and further satisfy boundary conditions beyond the non-confining ones at r=b. The region r&gt;b can then be filled with rf absorbing material and the hybrid modes will be severely attenuated. The cavity quality factor Q of the hybrid modes will be lowered to what turn out to be single digit values while the accelerating modes remain essentially unaffected.
One approach to deflection-mode damping is shown by U.S. Pat. No. 5,017,881 to Palmer. This device shows an accelerating cavity having iris structures for damping unwanted frequencies generated in the cavity. This accelerating cavity having slotted irises requires meticulous design of relatively large apertures in the waveguide walls, tuned to particular wavelengths of specific waveguide deflection modes, with a subsequent external waveguide required to propagate these deflection modes to far-removed attenuating loads.
In a preliminary prior art design of a mode trap by the inventor and others, Chojnacki et. al, Measurement of Deflection-Mode Damping in an Accelerating Structure, J. Appl. Phys. 69, May 1, 1991, and shown in FIG. 1, a multiplicity of longitudinal wires are located around the periphery of a dielectric tubular chamber for the beam with an absorber sleeve of nonmetallic material over the wire arrangement and within the conventional metal housing. Tests show that the accelerator mode is not significantly affected whereas the transverse mode is absorbed within a short time period. However, the interior dielectric is not as efficient overall as an iris-loaded waveguide for acceleration purposes, so its application is limited to a few special circumstances.
In an iris-loaded waveguide a similar prior art scheme can be employed by segmenting the outer conducting wall to allow only axial currents and also segmenting the irises so as to allow only radial currents as shown in FIG. 2. The close proximity of the iris aperture to the beam in this case, however, requires special attention to be given to field arcing and construction tolerances.
Arcing across segmented conductors would be due to the E.sub..theta. field which must be continuous there rather than zero.
There is a need for a transverse mode trap that suppresses the deflection or transverse modes without limiting the accelerator modes.
Accordingly, it is an object of the present invention to provide a transverse mode trap that suppresses the deflection or transverse modes without limiting the accelerator modes.
It is a further object of the present invention to provide a mode trap that reduces or eliminates arcing under the influence of high electric fields.
Yet another object of the present invention is to provide a mode trap that facilitates easy construction.